On Primary Relations at Tree-level in String Theory and Field Theory

Abstract

By the use of cyclic symmetry, KK relations and BCJ relations, one can reduce the number of independent $N$-point color-ordered tree amplitudes in gauge theory and string theory from $N!$ to $(N-3)!$. In this paper, we investigate these relations at tree-level in both string theory and field theory. We will show that there are two primary relations. All other relations can be generated by the primary relations. In string theory, the primary relations can be chosen as cyclic symmetry as well as either the fundamental KK relation or the fundamental BCJ relation. In field theory, the primary relations can only be chosen as cyclic symmetry and the fundamental BCJ relation. We will further show a kind of more general relation which can also be generated by the primary relations. The general formula of the explicit minimal-basis expansions for color-ordered open string tree amplitudes will be given and proven in this paper.

40 pages, 2 figures, major revised

References in corpus (35)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Explicit BCJ Numerators from Pure Spinors
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Open & Closed vs. Pure Open String Disk Amplitudes
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• On the Coupling of Gravitons to Matter
• Gravity and Yang-Mills Amplitude Relations
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Proof of Gravity and Yang-Mills Amplitude Relations
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• New Identities among Gauge Theory Amplitudes
• BCFW Recursion Relation with Nonzero Boundary Contribution
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• A Color Dual Form for Gauge-Theory Amplitudes
• Simplifying the Tree-level Superstring Massless Five-point Amplitude
• Six Open String Disk Amplitude in Pure Spinor Superspace
• New Relations for Gauge-Theory Amplitudes with Matter
• A note on the boundary contribution with bad deformation in gauge theory
• Monodromy--like Relations for Finite Loop Amplitudes
• KLT and New Relations for N=8 SUGRA and N=4 SYM
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure
• Comment on the Identities of the Gluon Tree Amplitudes
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation
• On tree amplitudes with gluons coupled to gravitons

Cited by in corpus (18)

• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Algebras for Amplitudes
• Amplitude Relations in Non-linear Sigma Model
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Tree-level amplitudes from the pure spinor superstring
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• The Complete KLT-Map Between Gravity and Gauge Theories
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• String theory in target space
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• BCJ, worldsheet quantum algebra and KZ equations
• Off-shell BCJ Relation in Nonlinear Sigma Model
• Note on off-shell relations in nonlinear sigma model
• Note on graph-based BCJ relation for Berends-Giele currents
• Boundary Behaviors for General Off-shell Amplitudes in Yang-Mills Theory
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• BCJ and KK Relations from BRST Symmetry and Supergravity Amplitudes
• A Tale Of Two Amplitudes In High Energy Physics